Question

Check If the equation is true or false .$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{n(n+1)}=\frac{n}{n+1}$

• A. True
• B. False

Answer 1

The correct option is A True

$a_n=\frac{1}{n(n+1)}{a}_n=\frac{n+1-n}{n(n+1)}{a}_n=\frac{n+1}{n(n+1)}-\frac{n}{n(n+1)}{a}_n=\frac{1}{n}-\frac{1}{n+1}$

$S_n=(1-\frac{1}{2})+(\frac{1}{2}-\frac{1}{3})+\dots (\frac{1}{n}-\frac{1}{n+1})S_n=1-\frac{1}{n+1}=\frac{n+1-1}{n+1}=\frac{n}{n+1}$